All Questions
Tagged with quantum-electrodynamics ward-identity
57
questions
3
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0
answers
74
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Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions
In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
- 51
1
vote
0
answers
55
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$Z_1=Z_2$ and its relation to vertex renormalization in QED
I have been working on the full renormalization of scalar QED with self-interactions, following the steps of Schwartz’s treatment on spinor QED (Chap 19). I have 3 main questions regarding this:
Need ...
- 162
0
votes
0
answers
48
views
Ward identity in scalar QED; gauge transformations & plane wave solutions for polarization
I am prepping for my QFT2 exam tomorrow, and in one of the mock exams I found the following question (and I'm not quite sure how to go about this). Given the following Lagrangian:
$$
L = -\frac{1}{4}...
1
vote
1
answer
90
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Three-point function general form
The general matrix element of the electromagnetic current can be written as $$iM^ {\mu} = \left< p^\prime,s^\prime | j^\mu (x) | p,s\right>=\bar{u}(p^\prime,s^\prime)\left( R(q^2) \gamma^{\mu} + ...
- 53
1
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0
answers
131
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Meaning of a Feynman diagram in proof of Ward-Takahashi identity in chapter 7 of Peskin and Schroeder
I'm trying to understand what the external photon in this diagram (page 238 in P&S) corresponds to exactly. This diagram is supposed to be a contribution to the Fourier transform of a QED ...
- 151
4
votes
2
answers
209
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Propagator and Ward identity in the $R_\xi$ gauge
The full gauge propagator in the $R_\xi$ gauge is
$$D_{\mu\nu} = \frac{i}{k^2+i\epsilon}\left(-g_{\mu\nu}+\frac{1-\xi}{k^2}k_\mu k_\nu\right).\tag{1}$$
Now if we take $\xi=0$, we get the Lorenz gauge, ...
2
votes
1
answer
101
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Charge renormalization using Ward identity
In Mandl & Shaw's Quantum Field Theory (p 181), the Ward identity
$$\frac{d\Sigma(p)}{dp_\mu} = \Lambda^\mu(p,p)\tag{9.60}$$
where $\Sigma(p)$ and $\Lambda^\mu (p^\prime,p)$ are respectively the ...
- 138
3
votes
0
answers
185
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Diagrammatic Ward Identity for the QED vertex
The QED Ward identity for the vertex reads
\begin{equation}
q^\mu\Gamma^\mu(p,p')=\Sigma(p)-\Sigma(p')
\end{equation}
with $q=p-p'$. In the limit $q\rightarrow 0$,
\begin{equation}
\Gamma^\mu(p,p)=\...
- 325
0
votes
1
answer
345
views
Faddeev-Popov trick in QED Peskin and Schroeder
On page 297 of Peskin and Schroeder, the book obtains the propogator
$$\tag{9.58} \tilde{D}_F^{\mu\nu}(k)=\frac{-i}{k^2+i\epsilon}\bigg(g^{\mu\nu}-(1-\xi)\frac{k^\mu k^\nu}{k^2}\bigg).$$
The book then ...
- 789
2
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answers
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How to use Ward identity to abbreviate the photon propagator into $\frac{-i\ g_{\mu\nu}}{q^2 (1- \Pi(q^2))}$?
How to derive abbreviated form (equation 7.75) from original form (equation 7.74) via Ward identity? (In Peskin's QFT Charpter 7 P246)
I still can't see this result after read this paragraph many ...
2
votes
0
answers
94
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Ward Identity, Green Function with Current Insertion and Amputated Green Function
The QED Lagrangian (for one fermion) is:
$$\mathcal{L} = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu} + \bar{\psi}\left(i \gamma^{\mu}\partial_{\mu} - m \right) \psi - q \bar{\psi} \gamma^{\mu}A_{\mu}\psi = \...
- 770
2
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0
answers
86
views
Does the Ward-Takahashi identity work for a virtual photon?
In the reaction of the transformation of an electron pair into a muon pair is performed Ward–Takahashi identity. Why if there is no interaction with a real photon?
- 51
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0
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115
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QED gauge invariance
On P & S page.297, in the second paragraph from bottom, the book discussed gauge invariance of Faddeev-Popov procedure, following
a QED example. Where the photon propagator is:
$$ \widetilde{D}_F^{...
- 1,421
4
votes
1
answer
399
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Ward-Takahashi Identity in QED
P&S write in Section 7.4 on page 238:
We will prove the Ward-Takahashi identity order by order in $\alpha$……The identity is generally not true for individual Feynman diagrams; we must sum over ...
- 1,421
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0
answers
57
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The presence of $\zeta^{\mu}(k)$ in the Ward-Takahashi identities in QED
On page 132 of Timo Weigand's QFT notes we introduce the Ward-Takahashi identity for QED, this is the statement that:
$$k^{\mu}\mathcal M_{\mu}(k)=0 \tag{5.35},$$
with
$$\mathcal M(k)=\zeta^{\mu}(k)\...
- 6,963